Current and upcoming cosmological experiments open a new era of precision cosmology, thus demanding accurate theoretical predictions for cosmological observables. Because of the complexity of the codes delivering such predictions, reaching a high level of numerical accuracy is challenging. Among the codes already fulfilling this task, PyCosmo is a Python-based framework providing solutions to the Einstein–Boltzmann equations and accurate predictions for cosmological observables. We present the first public release of the code, which is valid in ΛCDM cosmology. The novel aspect of this version is that the user can work within a Python framework, either locally or through an online platform, called PyCosmo Hub. In this work we first describe how the observables are implemented. Then, we check the accuracy of the theoretical predictions for background quantities, power spectra and Limber and beyond-Limber angular power spectra by comparison with other codes: the Core Cosmology Library (CCL), CLASS, HMCode and iCosmo. In our analysis we quantify the agreement of PyCosmo with the other codes, for a range of cosmological models, monitored through a series of unit tests. PyCosmo, conceived as a multi-purpose cosmology calculation tool in Python, is designed to be interactive and user-friendly. The PyCosmo Hub is accessible from this link: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html. On this platform the users can perform their own computations using Jupyter Notebooks without the need of installing any software, access to the results presented in this work and benefit from tutorial notebooks illustrating the usage of the code. The link above also redirects to the code release and documentation.